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  4. If the value of a third order determinant is 11 , then the value of the determinant formed by the cofactors will be

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Q. If the value of a third order determinant is $11 $ , then the value of the determinant formed by the cofactors will be

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Solution:

Determinant of the matrix of the cofactors is same as the determinant of the adjoint of the matrix, which is equal to $11^{2}=121 $
$\left(\because|\text{adj} A|=|A|^{n-1}\right)$